At many marine-terminating glaciers, the breakup of mélange, a floating aggregation of sea ice and icebergs, has been accompanied by an increase in iceberg calving and ice mass loss. Previous studies have argued that mélange may suppress calving by exerting a buttressing force directly on the glacier terminus. In this study, I adapt a discrete element model to explicitly simulate mélange as a cohesive granular material. Simulations show that mélange laden with thick landfast sea ice produces enough resistance to shut down calving at the terminus. When sea ice within mélange thins, the buttressing force on the terminus is reduced and calving is more likely to occur. When a calving event does occur, it initiates a propagating jamming wave within mélange, which causes local compression and then slow mélange expansion. The jamming wave can also initiate widespread fracture of sea ice and further increase the likelihood of subsequent calving events.

Sea-level rise may accelerate significantly if marine ice sheets become unstable. If such instability occurs, there would be considerable uncertainty in future sea-level rise projections due to imperfectly modeled ice sheet processes and unpredictable climate variability. In this study, we use mathematical and computational approaches to identify the ice sheet processes that drive uncertainty in sea-level projections. Using stochastic perturbation theory from statistical physics as a tool, we show mathematically that the marine ice sheet instability greatly amplifies and skews uncertainty in sea-level projections with worst-case scenarios of rapid sea-level rise being more likely than best-case scenarios of slower sea-level rise. We also perform large ensemble simulations with a state-of-the-art ice sheet model of Thwaites Glacier, a marine-terminating glacier in West Antarctica that is thought to be unstable. These ensemble simulations indicate that the uncertainty solely related to internal climate variability can be a large fraction of the total ice loss expected from Thwaites Glacier. We conclude that internal climate variability alone can be responsible for significant uncertainty in projections of sea-level rise and that large ensembles are a necessary tool for quantifying the upper bounds of this uncertainty.

[1] Understanding the mechanisms governing temporal variability of ice stream flow remains one of the major barriers to developing accurate models of ice sheet dynamics and ice-climate interactions. Here we analyze a simple model of ice stream hydrology coupled to ice flow dynamics and including drainage and basal cooling processes. Analytic and numerical results from this model indicate that there are two major modes of ice stream behavior: steady-streaming and binge-purge variability. The steady-streaming mode arises from friction-stabilized subglacial meltwater production, which may also activate and interact with subglacial drainage. The binge-purge mode arises from a sufficiently cold environment sustaining successive cycles of thinning-induced basal cooling and stagnation. Low prescribed temperature at the ice surface and weak geothermal heating typically lead to binge-purge behavior, while warm ice surface temperature and strong geothermal heating will tend to produce steady-streaming behavior. Model results indicate that modern Siple Coast ice streams reside in the binge-purge parameter regime near a subcritical Hopf bifurcation to the steady-streaming mode. Numerical experiments exhibit hysteresis in ice stream variability as the surface temperature is varied by several degrees. Our simple model simulates Heinrich event-like variability in a hypothetical Hudson Strait ice stream including dynamically determined purge time scale, till freezing and basal cooling during the binge phase. These findings are an improvement on studies of both modern and paleo-ice stream variability and provide a framework for interpreting complex ice flow models.Citation: Robel, A. A., E. DeGiuli, C. Schoof, and E. Tziperman (2013), Dynamics of ice stream temporal variability: Modes, scales, and hysteresis,

ABSTRACT. Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback -wherein faster ice flow leads to higher rates of shear heating, further softening the ice -is a fundamental control on glacier dynamics.

ABSTRACT. Ocean tides influence the flow of marine-terminating glaciers. Observations indicate that the large fortnightly variations in ice flow at Rutford Ice Stream in West Antarctica originate in the floating ice shelf. We show that nonlinear variations in ice shelf buttressing driven by tides can produce such fortnightly variations in ice flow. These nonlinearities in the tidal modulation of buttressing stresses can be caused by asymmetries in the contact stress from migration of the grounding line and bathymetric pinning points beneath the ice shelf. Using a simple viscoelastic model, we demonstrate that a combination of buttressing and hydrostatic stress variations can explain a diverse range of tidal variations in ice shelf flow, including the period, phase and amplitude of flow variations observed at Rutford and Bindschadler Ice Streams.

Increasing surface melt has been implicated in the collapse of several Antarctic ice shelves over the last few decades, including the collapse of Larsen B Ice Shelf over a period of just a few weeks in 2002. The speed at which an ice shelf disintegrates strongly determines the subsequent loss of grounded ice and sea level rise, but the controls on collapse speed are not well understood. Here we show, using a novel cellular automaton model, that there is an intrinsic speed limit on ice shelf collapse through cascades of interacting melt pond hydrofracture events. Though collapse speed increases with the area of hydrofracture influence, the typical flexural length scales of Antarctic ice shelves ensure that hydrofracture interactions remain localized. We argue that the speed at which Larsen B Ice Shelf collapsed was caused by a season of anomalously high surface meltwater production.

Observations indicate that the grounding line position of West Antarctica is sensitive to both forced and unforced ice stream variabilities. This study endeavors to characterize and understand unforced ice stream variability and associated grounding line migration. We use a flowline ice stream model with an undrained plastic bed, lateral shear stresses, and a stretched grid refined in the grounding zone. This model exhibits parameter space structure and hysteresis behavior similar to simpler ice stream models. Low prescribed temperature at the ice surface or weak geothermal heating produces thermal oscillations between active and stagnant phases. As in previous spatially resolved ice flow models, thermal activation propagates as an “activation wave.” This model's fine resolution of the grounding zone allows for accurate simulations of transient, unforced grounding line migration. Upstream of the grounding zone, horizontal grid spacing of 1 km is required to accurately resolve activation waves. Activation waves induce the grounding line to migrate over 100 km at a rate that can exceed 1 km/yr. This is followed during the active phase by retreat, which then continues for the duration of the stagnant phase. Grounding line retreat is the result of a negative mass balance near the grounding line but is not necessarily associated with negative mass balance for the entire ice stream in our simulations of internal variability. The novel approach and experiments described in this study show that there can be large excursions in grounding line position in the absence of either external forcing or retrograde slopes.

Increasing surface melt has been implicated in the collapse of several Antarctic ice shelves over the last few decades, including the collapse of Larsen B Ice Shelf over a period of just a few weeks in 2002. The speed at which an ice shelf disintegrates strongly determines the subsequent loss of grounded ice and sea level rise, but the controls on collapse speed are not well understood. Here we show, using a novel cellular automaton model, that there is an intrinsic speed limit on ice shelf collapse through cascades of interacting melt pond hydrofracture events. Though collapse speed increases with the area of hydrofracture influence, the typical flexural length scales of Antarctic ice shelves ensure that hydrofracture interactions remain localized. We argue that the speed at which Larsen B Ice Shelf collapsed was caused by a season of anomalously high surface meltwater production.